A rectangle is x cm long and 5cm broad. Its perimeter is p cm, where 14≤x≤32. Find the corresponding values of x.
The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width of the rectangle.
In this case, we are given that the length of the rectangle is x cm and the width is 5 cm. So, the perimeter is P = 2(x) + 2(5) = 2x + 10 cm.
We are also given that the perimeter is p cm, so we have the equation 2x + 10 = p.
Given that 14 ≤ x ≤ 32, we can solve for the corresponding values of x by substituting different values of p into the equation and solving for x.
For example, let's say p = 30.
Substituting p = 30 into the equation, we have 2x + 10 = 30.
Simplifying the equation, we get 2x = 20.
Dividing both sides of the equation by 2, we have x = 10.
Therefore, when p = 30, the corresponding value of x is 10.
We can repeat this process for different values of p to find the corresponding values of x.